Hole Locations and a Filling Method for Coprime Planar Arrays for DOA Estimation

Coprime linear arrays (CLAs) have drawn lots of attention. Efforts have been made to reveal the hole locations in the difference coarrays of CLAs, based on which many methods have been proposed to fill the holes, lengthening the consecutive difference coarray part and increasing the effective degrees of freedom (DOFs). Compared with CLAs, two dimensional (2D) coprime planar arrays (CPAs) are more relevant to real applications. However, no closed-form expressions for the hole locations in the difference coarray of a CPA have been found in the open literature, and the advantage in terms of DOFs of CPAs has not been well explored. In this letter, the structure of the difference coarrays of CPAs is investigated and the exact expressions of all hole positions are provided. Then, a holes-filling method is proposed, by which the most critical holes in the difference coarray can be filled such that a difference coarray with more consecutive lags as well as higher effective DOFs can be obtained.